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The new result, from Yitang Zhang of the University of New Hampshire in Durham, finds that there are infinitely many pairs of primes that are less than 70 million units apart without relying on unproven conjectures. Although 70 million seems like a very large number, the existence of any finite bound, no matter how large, means that that the gaps between consecutive numbers don’t keep growing forever. The jump from 2 to 70 million is nothing compared with the jump from 70 million to infinity. “If this is right, I’m absolutely astounded,” says Goldfeld.